How can I send variables to Jinja template from a Flask decorator?

You can use a context processor (http://flask.pocoo.org/docs/api/#flask.Flask.context_processor):

def include_sidebar_data(fn):
    @blueprint.context_processor
    def additional_context():
        # this code work if endpoint equals to view function name
        if request.endpoint != fn.__name__:
            return {} 
        var1, var2, var3 = generate_sidebar_data()
        return {
            'var1': var1,
            'var2': var2,
            'var3': var3,
        }
    return fn


@blueprint.route('/')
@include_sidebar_data
def frontpage():
    return render_template('template.html')

UPD: I like the next example more and it is better if the decorator is used for several view functions:

sidebar_data_views = []


def include_sidebar_data(fn):
    sidebar_data_views.append(fn.__name__)
    return fn


@blueprint.context_processor
def additional_context():
    # this code work if endpoint equals to view function name
    if request.endpoint not in sidebar_data_views:
        return {} 
    var1, var2, var3 = generate_sidebar_data()
    return {
        'var1': var1,
        'var2': var2,
        'var3': var3,
    }


@blueprint.route('/')
@include_sidebar_data
def frontpage():
    return render_template('template.html')

I'm going to propose something even simpler than using a decorator or template method or anything like that:

def render_sidebar_template(tmpl_name, **kwargs):
    (var1, var2, var3) = generate_sidebar_data()
    return render_template(tmpl_name, var1=var1, var2=var2, var3=var3, **kwargs)

Yup, just a function. That's all you really need, isn't it? See this Flask Snippet for inspiration. It's essentially doing exactly the same sort of thing, in a different context.